
These constraints ensure that the whole intensity range is covered and the response function is smooth.
Overexposed and underexposed pixels are clamped to the maximum and minimum output values of 1 and 0.
This matches digital camera behavior, however we found that an end-to-end training of the rendering pipeline is not reliable when implementing the clamping.
Depending on the random network initialization, it is possible that the whole image is over/under exposed generating a zero gradient over the complete image.
Inspired by the LeakyReLU activation function [1]}, we define a separate response function \(R_t\)  during training that leaks small values instead of clamping them.
\(R_{t}(x) ={\left\lbrace \begin{array}{ll}\alpha x & x < 0 \\R(x) & 0\le x\le 1 \\\end{array}\frac{-\alpha }{\sqrt{x}}+\alpha + 1 & 1 < x\right.}\) 
